CN111581874A - Method for solving laser processing track of thin-wall curved surface layer pattern - Google Patents

Method for solving laser processing track of thin-wall curved surface layer pattern Download PDF

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CN111581874A
CN111581874A CN202010599362.2A CN202010599362A CN111581874A CN 111581874 A CN111581874 A CN 111581874A CN 202010599362 A CN202010599362 A CN 202010599362A CN 111581874 A CN111581874 A CN 111581874A
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马建伟
姜文文
贾振元
韩东旭
王健
王福吉
刘巍
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Dalian University of Technology
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Abstract

The invention discloses a method for solving a laser processing track of a thin-wall curved surface layer pattern, belongs to the technical field of precision manufacturing of the thin-wall curved surface layer pattern, and relates to the method for solving the laser processing track of the thin-wall curved surface layer pattern. According to the method, according to the clamping deformation characteristics of the thin-wall curved surface piece, the point cloud data of the clamped curved surface is obtained through a three-coordinate measuring machine, the point cloud data is mapped to the ideal curved surface along the radial direction, the triangular mesh mapping relation of the clamped curved surface and the ideal curved surface is constructed, and the mapping track of the ideal processing track on the clamped curved surface is solved. According to the laser ablation size prediction model, the ablation depth and the ablation width of the material at any cutter position on the mapping track are solved in a discretized mode, instantaneous machining parameter change caused by curve curvature change is considered, local machining track point adjustment is conducted on the pattern curve size or the outline tolerance position, and finally the five-axis numerical control machining track conforming to machining precision is generated. The method reduces the processing error caused by clamping deformation, and is suitable for precision processing of the surface layer pattern of the thin-wall curved surface.

Description

Method for solving laser processing track of thin-wall curved surface layer pattern
Technical Field
The invention belongs to the technical field of precision manufacturing of thin-wall curved surface patterns, and relates to a method for solving a laser processing track of a thin-wall curved surface pattern.
Background
With the development of the fields of aerospace, information transmission and the like, a functional integrated part with a complex curved surface structure required for electromagnetic wave transmission control gradually becomes an important component form. The high-speed aircraft antenna is an important application of the components, and in order to meet the requirements of high performance and light weight, the antenna mostly adopts a light material thin-wall curved surface base body structure, and the requirement of machining precision is generally in the micron order, so that a new challenge is provided for the existing machining technology. The efficient and high-precision manufacture of complex patterns on the surfaces of thin-wall curved surface parts is still a hotspot and a difficulty of research. The laser etching processing technology, which has been rapidly developed in recent years, has become an effective method for precisely and efficiently manufacturing surface patterns of complex curved surface members due to its advantages such as non-contact processing and easy coupling with a multi-axis driving device. However, the thin-wall curved surface part has low rigidity and is easy to generate elastic deformation in a clamping state, so that the deviation between an actual processing curved surface and an ideal curved surface is generated, and if the processing is carried out according to a processing track planned by an ideal antenna pattern, the outline and the position of an antenna pattern curve after clamping and releasing are not in accordance with the original design. In addition, the curvature of the thin-wall curved surface is changed after deformation, and laser technological parameters are changed in the processing process, so that the processing size precision of the antenna pattern is influenced. Therefore, a method for solving the laser processing track of the surface layer pattern of the thin-wall curved surface is urgently needed to be researched, the mapping track of the ideal processing track of the pattern on the curved surface in the clamping state is solved, the influence of curvature change after the curved surface is deformed on laser process parameters is considered, the out-of-tolerance point of the processing track is adjusted by taking the contour precision and the size precision of the curve of the processing pattern as constraints, and the precise processing of the surface layer pattern of the thin-wall curved surface is realized.
Prior art document 1 "correlation of work piece deformation used by reusing the clamping force", Shao Xiaodong et al, Transactions of the Canadian Society for mechanical Engineering, 2013, 37: 703-712, the document proposes a processing trajectory mapping method based on a tetrahedral mesh model, which establishes a mapping relationship between finite element meshes before and after deformation by a finite element method, and solves the processing trajectory of the deformed workpiece according to the similarity transformation principle, thereby improving the processing precision of the thin-wall part. However, in a real situation, clamping deformation is affected by the clamping sequence and the clamping force, stability is poor, and a new error is introduced by adopting a simulation analysis method. Prior art document 2 "Adaptive mapping for curved surface based on-Machine measurement and ideal mapping", Bi Qingzhen et al, International journal of Machine Tools and artifacts, 2019, 136: 34-44, the document provides a curved surface matching method for a large thin-wall skin curved surface, the deformed curved surface measurement point cloud is projected to a standard curved surface to obtain an initial matching point, a mapping relation between the standard curved surface and the deformed curved surface is iteratively constructed based on a curved surface matching algorithm of equidistant mapping, and a processing track is adaptively adjusted according to the mapping relation, and experimental results show that the method effectively improves the processing contour precision. However, the method is only suitable for large thin-wall skin curved surface workpieces with deformation mainly along the normal direction, and the curved surface matching algorithm needs a large amount of iterative computation and is complex and time-consuming.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for solving the laser processing track of a thin-wall curved surface pattern. The method comprises the steps of firstly establishing a mapping relation between a clamping state curved surface and an ideal curved surface, solving a mapping track of the ideal track on the clamping state curved surface, analyzing local track laser processing process parameter change caused by curvature change of the clamping state curved surface, combining a laser ablation size prediction model, adjusting the processing track by taking surface layer pattern processing precision requirements as constraints, and ensuring the processing size precision and contour precision of a thin-wall curved surface layer pattern curve.
The technical scheme adopted by the invention is a method for solving the laser processing track of the surface pattern of the thin-wall curved surface, which is characterized in that firstly, the method proposes the hypothesis that the clamping deformation is mainly along the radial direction according to the clamping deformation characteristics of a thin-wall curved surface piece, obtains the point cloud data of the clamped curved surface by a three-coordinate measuring machine, maps the point cloud data to an ideal curved surface along the radial direction, respectively constructs the triangular mesh mapping relation between the clamped curved surface and the ideal curved surface, solves the mapping track of the ideal processing track on the clamped curved surface, then, according to a laser ablation size prediction model, discretely solves the material ablation depth and the ablation width at any cutter position on the mapping track, considers the instantaneous process parameter change caused by the curvature change of the curved surface, carries out the adjustment of the local processing track point at the size of the pattern curve or the outline over-tolerance, and finally generates the five-, the method comprises the following specific steps:
step 1, constructing a triangular mesh mapping relation between a clamping state curved surface and an ideal curved surface
First, in the Ansys software, a coordinate system is established with the center of circle of the cylinder bottom end surface 2 as the origin, the cylinder bottom end surface 2 is an XOY plane, and the cylinder axis is a Z axis. The thin-wall cylindrical part is clamped in the radial direction, and the clamping force is symmetrically distributed in the circumferential direction. Workpiece clamping deformation is simulated by adopting Ansys finite element analysis software, a four-node shell181 unit model is established in Ansys, material attributes are set, and a free grid division mode is adopted. At 4 clamping points J1、J2、J3、J4Applying a concentrated load, setting full constraint on the upper end surface 1 of the cylinder, and solving the current load and the result under the constraint; and viewing the result under the post-processing interface setting in a cylindrical coordinate system, wherein the x direction represents the radial direction, the y direction represents the tangential direction, and the z direction represents the axial direction. And (3) exporting the calculation result of the node deformation, calculating the deviation value between the radial deformation and the total deformation of each node, considering that the deformation is mainly in the radial direction if the deviation value is smaller than the total deformation by one order of magnitude, and providing the assumption that the clamping deformation of the thin-wall cylindrical part is mainly in the radial direction.
According to the assumption that the clamping deformation of the thin-wall cylindrical part is mainly along the radial direction, the three-coordinate measuring machine is used for measuring to obtain the discrete point cloud of the thin-wall cylindrical part in a clamping state, and the discrete point cloud is mapped onto the ideal curved surface along the radial direction, so that the only mapping point of the measuring point in the ideal curved surface can be solved. And performing triangulation on the discrete point cloud of the clamped curved surface, constructing a triangular mesh curved surface of the clamped cylindrical triangular mesh, and constructing a triangular mesh unit of an ideal curved surface in the same topological relation according to the mapping point cloud. Therefore, the mapping relation between the measuring points and the mapping points is converted into the mapping relation between the vertexes of the curved surfaces of the two triangular meshes, and the mapping relation between the clamped curved surface and the ideal curved surface is established.
Step 2, solving the mapping track of the ideal track in the clamping state curved surface
And solving the mapping relation between the ideal curved surface mesh and any point on the clamped curved surface mesh by the triangular affine transformation theory. Generating ideal tool location points on an ideal curved surface according to an original design pattern, and enabling one ideal tool location point to be Wi(i ═ 1, 2.. once, n), where n is the number of knife points, finding the triangle patch where it is located in the ideal surface mesh according to the coordinate value of knife points, and making the vertex coordinate of the triangle patch be Qi,Mi,Ni. Ideal tool location point WiAt Δ QiMiNiThe area coordinate in (A) can be expressed as Wi(λ1,λ2,λ3) Then point WiSatisfies the formula (1), and λ1+λ2+λ3＝1。
(λ1+λ2+λ3)Wi＝λ1Qi+λ2Mi+λ3Ni(1)
Point WiAnd Δ QiMiNiEach vertex will be Δ QiMiNiDivided into Δ QiMiWi，ΔMiNiWi，ΔQiNiWiHaving an area of
Figure BDA0002558659820000041
From the properties of the triangular area coordinates:
Figure BDA0002558659820000042
triangular patch delta Q in an ideal mesh surfaceiMiNiThe mapping triangular patch in the clamped state mesh surface is delta Q'iM′iN′iFrom the area coordinate invariance according to the triangle affine transformation, Δ Q can be foundiMiNiInner arbitrary knife position WiIn delta Q'iM′iN′iInner mapped knife location point W'iThe coordinates of (a) are:
W′i＝λ1Q′i+λ2M′i+λ3N′i(3)
and establishing an ideal model of the thin-wall cylindrical part in UG, drawing a pattern curve on the surface of the workpiece, projecting the pattern curve on the surface of the workpiece, and generating a five-axis machining track in a curve driving mode. Deriving the knife location and calculating from the formulas (1) - (3)
And solving the mapping point of the machining trajectory on the clamped state curved surface to realize the mapping of the machining trajectory.
Step 3, establishing an ablation size prediction model
And establishing a laser ablation size prediction model, facilitating subsequent discretization to solve the material ablation depth and the ablation width at any cutter position on the mapping track, and judging the track over-differential point. The nanosecond laser is adopted for processing, and the distribution of laser energy density of a light beam on an x-z section can be expressed as follows:
Figure BDA0002558659820000051
wherein w is the actual spot size, F0The peak energy density for a beam acting on an x-z cross-section can be calculated by:
Figure BDA0002558659820000052
in the formula
Figure BDA0002558659820000053
F is the pulse repetition frequency of the laser, which is the average power of the laser.
The spot size w of the beam at any position in the z direction can be expressed as:
Figure BDA0002558659820000054
in the formula, w0λ is the wavelength of the laser light, which is the spot size of the beam at the beam waist position.
When the energy density of the pulse laser exceeds the ablation threshold of the material, the evaporation phenomenon appears on the surface of the material in the laser action area to remove the formed material, and the process conforms to the energy conservation law:
(1-R)F(x,z)-Fth＝(x,z)(ρsHsl+ρlHlv) (7)
wherein R is the reflectivity of the target material to the laser, rholIs the liquid density of the target material, HlvIs the enthalpy of vaporization of the target material, HslIs the melting enthalpy of the target material, FthAnd F (x, z) is the energy density distribution of the beam in an x-z section, and when the defocusing amount of the single-pulse laser beam acting on the surface of the material is z, the ablation depth of the material at any point on the x-z section is recorded as the ablation depth of the single-pulse laser.
The single-pulse ablation depth (x, z) can then be expressed as:
Figure BDA0002558659820000061
the distance and direction of the light spot of the light beam acting on the surface of the material, which deviates from the focal plane, determine the size of the light spot of each pulse laser acting on the surface of the material. When z is a negative value, the laser beam focal plane is above the material surface and is marked as negative defocus; when z is positive, the laser beam focal plane is below the material surface, noted as positive defocus.
When the scanning speed of the pulsed laser is v, the number N of laser pulses acting on a certain position can be expressed as:
Figure BDA0002558659820000062
where int is a floor function. The laser beam gradually diverges during propagation, and the divergence of the beam can be expressed by the differential equation of the spot size:
Figure BDA0002558659820000063
the divergence angle theta of the laser light at a certain position (x, z)*Comprises the following steps:
Figure BDA0002558659820000064
passing position (x)k-1,zk-1) Before ablation of the kth laser pulse, the defocus z of the beamk-1Can be expressed as:
zk-1＝z0+k-1(12)
in the formula, z0Is the initial amount of defocus of the beam,k-1is the sum of the ablation depths of the first k-1 pulses.
Past the ablation site (x)k-1,zk-1) The single pulse energy distribution of the kth laser pulse of (a) may be expressed as:
Figure BDA0002558659820000065
calculated ablation position (x)k-1,zk-1) Laser divergence angle theta of*(xk-1,zk-1) Can be expressed as:
Figure BDA0002558659820000066
the ablation is carried out along the propagation direction of the laser, passing through the ablation site (x)k-1,zk-1) The k-th laser pulse ablation depth of (c) can be expressed as:
Figure BDA0002558659820000071
two spatial positions (x) before and after ablationk-1,zk-1) And (x)k,zk) The following geometrical relationships exist:
Figure BDA0002558659820000072
let N be 2N +1, the cross-sectional dimension of the pulsed laser ablated target material can be expressed as:
Figure BDA0002558659820000073
when x is 0, the ablation depth reaches a maximum value, which is depth (0).
The position when depth (x) is 0 is the edge of ablation outline, the distance between two side edges is maximum ablation width, let x be depth-1(x) Is the inverse function of depth (x), when depth (x) is 0, the two solutions of the inverse function are x1，x2Then the maximum ablation width is | x1-x2|。
Step 4, mapping track adjustment considering the curvature change of the curved surface
And (3) combining an ablation size prediction model, considering instantaneous processing process parameter change caused by curved surface curvature change, and performing local mapping processing track point adjustment on the size or contour out-of-tolerance part of the pattern curve.
Two adjacent knife location points W 'of mapping track'i、W′i+1The curve of the curved surface between the two surfaces along the feeding direction is simplified into a radius R1Arc of (2), mixing'i、W′i+1The inter-ideal pattern curve is simplified to radius R2Is used for the arc of (1). Combining a nearest neighbor search algorithm and a least square surface fitting method to pair W'iAnd performing least square surface fitting on the adjacent points, wherein the surface parameter equation is expressed as r (u, v), and the first basic form and the second basic form of the surface r (u, v) can be expressed as:
Figure BDA0002558659820000074
wherein the coefficients E, F, G, L, M, N are:
Figure BDA0002558659820000081
wherein
Figure BDA0002558659820000082
Is curved surface r (u, v) is W'iThe unit normal vector of a point can be calculated by:
Figure BDA0002558659820000083
the principal curvature and principal direction of the curved surface r (u, v) are the eigenvalues and the eigendirections of the Weingarten matrix ω, which can be expressed as:
Figure BDA0002558659820000084
solving the eigenvalue and the eigen direction of the Weingarten matrix omega to obtain the maximum principal curvature k of the curved surface r (u, v)1The corresponding main direction is d1Minimum principal curvature of k2The corresponding main direction is d2. Let the feeding direction
Figure BDA0002558659820000085
And a main direction d1Is at an included angle of
Figure BDA0002558659820000086
The normal curvature in the feed direction, i.e. the adjacent cutting location W ', can be determined from the Euler equation'i、W′i+1Curvature k of curved surface between the two surfaces along the feeding directionn：
Figure BDA0002558659820000087
W'iIs taken as the origin point of the image,
Figure BDA0002558659820000088
direction x0Shaft, W'iNormal vector direction on the surface of clamped state
Figure BDA0002558659820000089
Is z1And establishing a local dynamic plane rectangular coordinate system. During machining, the laser beam is guided from the knife position W'iGo to W'i+1In time, the initial defocusing amount z of laser processing at any position of the track0Can be calculated from the following formula:
Figure BDA00025586598200000810
laser beam from knife location point W'iGo to W'i+1In the process of (3), the actual scanning speed v' can be calculated by the following formula:
Figure BDA0002558659820000091
according to the laser ablation size prediction model, the W 'can be obtained by iterative calculation of Matlab software'iTo W'i+1The ablation depth of the material at any position of the motion track of the point is depth (x)0) Ablation width of width (x)0)。
Then, during machining, the light beam is emitted from the knife position W'iThrough W'i+1In the process of (1), W'i、W′i+1The ablation depth error DE at any position along the curve of the curved surface in the feed direction can be expressed as:
DE＝depth(x0)-depth(0) (25)
due to the change of the curvature of the clamping state curved surface, the distance between two adjacent cutter positions of the processing track mapped to the clamping state curved surface is also changed, and deviation, namely contour deviation, is generated between an actual processing curve and an ideal curve.
And (3) interpolating a graph curve of the ideal antenna pattern on the clamped state curved surface by using a cubic B-spline interpolation method and through the characteristic points, namely the back-calculation control points mapped to the track points of the clamped state curved surface. The NURBS rational fraction form of the cubic B-spline curve is:
Figure BDA0002558659820000092
in the formula, ωi(i ═ 0, 1.. n) is a weight factor, and the first weight factor and the last weight factor are omega0,ωn> 0, the rest omegai≥0，Ai(i ═ 0, 1.. times, n) is a control point, B is a control pointi,k(u) is a k-order canonical B-spline basis function, u is a parameter value, knife location W'iCorresponding parameter value is ui。
Then the clamped state curved surface ideal antenna curve is at a knife position point W'iRadius of curvature R of2Can be calculated from the following formula:
Figure BDA0002558659820000093
based on adjacent knife location point W'i、W′i+1An ideal curve is calculated, a local plane rectangular coordinate system is established, and then W'i、W′i+1The inter-ideal curve equation can be expressed as:
Figure BDA0002558659820000101
after processing, W'i、W′i+1The actual curve equation between can be expressed as:
z3＝width(x0)-width(0) (29)
then, during machining, the light beam is emitted from the knife position W'iThrough W'i+1The profile deviation CR between the actual machining curve and the ideal curve can be expressed as:
CR＝z3-z2(30)
the tolerance value for the ablation depth error is expressed as [ DE ]]The deviation tolerance value of the curve profile of the pattern is expressed as [ CR]Adjacent knife location point W 'is programmed to be calculated by Matlab software'i、W′i+1Ablation depth error DE of inter-trackiAnd pattern curve profile deviation CRiAnd judging whether the distance is within the tolerance range, if the distance is out of tolerance, adding a knife position W' between the two knife positionsu＝u'Wherein the parameter u ═ ui+ui+1) And/2, continuously judging, and if the position is within the tolerance range, calculating the cutter position W'i、W′i+2Ablation depth error DE of inter-trackiiAnd the profile deviation CR of the pattern curveiiRemoving the redundant point W 'if the tolerance range is met'i+1And continuing to judge, and finally solving to obtain the tool location point data meeting the precision requirement.
Step 5, solving and generating five-axis numerical control machining track based on machine tool forward and inverse kinematics
The adjusted tool position data points cannot generate a five-axis machining program which can be identified by the machine tool through a post-processing module of UG software, so that the positive and negative kinematics solution needs to be carried out on the laser-five-axis numerical control machine tool system in order to convert the adjusted tool position data into the motion data of each axis of the machine tool.
OMXMYMZMFor a coordinate system fixedly connected with the machine tool body, the tool location point and the tool shaft direction are relative to the machine tool coordinate system O in kinematic transformationMXMYMZMAre respectively homogeneous coordinates ofMP andMand V. The laser processing is non-contact processing without a solid cutter, and the cutter shaft direction is the laser beam propagation direction.
OAXAYAZAIs a coordinate system fixedly connected with the fixed axis A, and has an origin OAIn the coordinate system OMXMYMZMHas the coordinates of (U)max,Umay,Umaz) O when the machine moves to the (X, Y, Z, A, C) positionAXAYAZAWill rotate around its own X-axis by an angle-A, OAXAYAZARelative to OMXMYMZMPosition and posture of
Figure BDA0002558659820000111
Comprises the following steps:
Figure BDA0002558659820000112
OCXCYCZCis a coordinate system fixedly connected with the fixed axis C, the origin OCIn the coordinate system OAXAYAZAHas the coordinates of (U)acx,Uacy,Uacz) O when the machine moves to the (X, Y, Z, A, C) positionCXCYCZCWill rotate around its own Z axis by an angle of-C, then OCXCYCZCRelative to OAXAYAZAPosition and posture of
Figure BDA0002558659820000113
Comprises the following steps:
Figure BDA0002558659820000114
OWXWYWZWfor a coordinate system of the workpiece fixedly connected to the workpiece, origin OWAnd OCCoincidence, then OWXWYWZWRelative to OCXCYCZCPosition and posture of
Figure BDA0002558659820000115
Comprises the following steps:
Figure BDA0002558659820000116
homogeneous coordinates of the tool location point and the tool shaft direction in the workpiece coordinate systemWP andWv is respectively:
Figure BDA0002558659820000117
for the adjusted tool location point, the tool axis direction needs to be solved. A certain knife position point Pi(x, y, z) and the points nearby are fitted with a least square surface to solve the tool positionThe normal vector of the point on the curved surface, the normal vector direction
Figure BDA0002558659820000118
Namely the cutter shaft direction of the cutter location point under the workpiece coordinate system.
OTXTYTZTFor a tool coordinate system fixedly connected to the laser, OTXTYTZTRelative to OMXMYMZMPosition and posture of
Figure BDA0002558659820000121
Comprises the following steps:
Figure BDA0002558659820000122
homogeneous coordinate of tool location point and tool shaft direction in tool coordinate systemTP andTv is respectively:
Figure BDA0002558659820000123
and respectively mapping the tool location points from the tool coordinate system and the workpiece coordinate system to the machine tool coordinate system through homogeneous transformation:
Figure BDA0002558659820000124
solving to obtain the homogeneous coordinates of the cutter location point and the cutter shaft direction under the workpiece coordinate systemWP andWv is respectively:
Figure BDA0002558659820000125
obtaining an inverse transformation formula from a workpiece coordinate system to a machine tool coordinate system through machine tool inverse kinematics transformation:
Figure BDA0002558659820000126
wherein, the motion range of the A axis is-5 degrees to 95 degrees, the angle of the C axis can be any value, and in order to avoid the solution of the A from exceeding the motion range or the discontinuity of the machine tool rotation angle C caused by multiple solutions of the angle of the C axis, the A, C angle is corrected as follows:
Figure BDA0002558659820000127
the adjusted tool position data can be converted into the motion data of each axis of the machine tool by the formulas (39) - (40), and then a five-axis numerical control machining program of the surface layer pattern of the clamping state curved surface is generated.
The method has the advantages that the method clarifies the clamping deformation characteristic of the thin-wall curved surface piece, and can quickly and accurately solve to obtain the mapping track of the ideal processing track in the clamping state curved surface; the method analyzes the applicability of the mapping track to the deformed curved surface, considers the influence of the curvature change of the curved surface caused by deformation on the laser processing technological parameters of the mapping track, and combines a laser ablation size prediction model to adjust the local over-tolerance point and the redundant point of the track, thereby finally generating the laser processing track of the surface layer pattern of the thin-wall curved surface in the clamping state which meets the precision requirement. The method solves the problems of processing position deviation, laser process parameter change, non-conformity of the processing pattern outline with the original design, excessive ablation or insufficient ablation of the pattern and the like caused by clamping deformation in the laser processing process of the surface pattern of the thin-wall curved piece, can reduce the laser processing error of the surface pattern of the thin-wall curved piece caused by the clamping deformation, and has important significance for realizing the fine manufacturing of the surface pattern of the thin-wall curved piece.
Drawings
FIG. 1-flowchart of the overall process.
Figure 2-thin-walled cylinder load and restraint application. Wherein, 1-cylinder upper end face, set up the full constraint on this end face, namely the degree of freedom of all directions is 0, 2-cylinder bottom end face, the coordinate system regards bottom surface circle centre of a circle of cylinder as the origin, the bottom surface is the xoy plane, the cylinder axis is the z axle; in the figure, the thin-walled cylinder part has 4 clamping points J in the section of 0.03m from the bottom of the cylinder1、J2、J3、J4。
FIG. 3 shows a simulation result of clamping deformation of a thin-walled cylindrical part. Wherein, the graph a) is a radial deformation cloud picture, the graph b) is a tangential deformation cloud picture, the graph c) is an axial deformation cloud picture, the graph d) is a total deformation cloud picture, and the unit of deformation is m.
Fig. 4-ideal machining trajectory tool position diagram.
FIG. 5-map trajectory tool bit map.
FIG. 6 is a flowchart of a tool position adjustment procedure.
Fig. 7-tool position diagram of the processing path after mapping and adjustment. Wherein, the coordinate unit of the knife position point is mm, the "·" in the figure shows the knife position point of the mapping track, the "+" shows the added knife position point, and the "o" shows the removed redundant knife position point.
Detailed Description
The detailed description of the embodiments of the invention is provided with reference to the accompanying drawings.
Example (b): the selected material is 6061 aluminum alloy, the elastic modulus of the material is 71700MPa, the Poisson ratio is 0.33, the outer diameter of the thin-wall cylindrical part is 0.098m, the height of the thin-wall cylindrical part is 0.15m, the thickness of the thin-wall cylindrical part is 0.001m, a seven-leaf plum curve is processed on the surface of the thin-wall cylindrical part, and the implementation process of the invention is described in detail below.
Aiming at the problem that the thin-wall curved surface piece is low in rigidity and easy to generate elastic deformation in a clamping state, and a pattern curve processing error is easy to cause in the processing process of a thin-wall curved surface pattern, the invention provides a method for solving the laser processing track of the thin-wall curved surface pattern, and the whole flow of the method is shown in figure 1.
Firstly, a coordinate system is established in the Ansys software by taking the center of a circle of the bottom surface 2 of the cylinder as an origin, the bottom surface is an XOY plane, and the axis of the cylinder is a Z axis. Modeling is performed on the thin-wall cylindrical part, and the constraint and applied load conditions of the thin-wall cylindrical part are shown in figure 2. The cylinder upper end face 1 is set to be fully constrained, i.e., the degree of freedom in each direction is 0. 4 clamping points J are arranged on a section at a distance of 0.03m from the cylinder bottom 21、J2、J3、J4The clamping force is symmetrically distributed on the circumferential surface of the cylinder body at 90 degrees, and the clamping radial force is 150N.
The method comprises the following specific steps:
step 1, constructing a triangular mesh mapping relation between a clamping state curved surface and an ideal curved surface
And (5) simulating the clamping process of the thin-wall cylinder, and solving the result under the current load and constraint. And viewing a solving result in the post-processing interface under a cylindrical coordinate system, wherein the x direction represents the radial direction, the y direction represents the tangential direction, and the z direction represents the axial direction. The simulation result of the clamping deformation of the thin-wall cylindrical part is shown in fig. 3. The drawing a) is a radial deformation cloud picture, the drawing b) is a tangential deformation cloud picture, the drawing c) is an axial deformation cloud picture, and the drawing d) is a total deformation cloud picture, wherein the unit of deformation is m. According to the simulation result, the trend of the total deformation is consistent with that of the radial deformation, the deformation amount is large near the middle point of the arcs between the four clamping points and the two adjacent clamping points, the axial deformation and the tangential deformation are relatively small, and the calculation results of the total deformation and the radial deformation of the node are derived. Calculating the deviation value between the radial deformation and the total deformation of each node, wherein the deviation value is smaller than the total deformation by one order of magnitude, considering that the deformation is mainly in the radial direction, calculating to obtain that 96% of the node deformation is mainly in the radial direction, and considering only the nodes with larger deformation, almost all the node deformation is mainly in the radial direction, so that the assumption that the clamping deformation of the thin-wall cylindrical part is mainly in the radial direction is provided. And then measuring by using a three-coordinate measuring machine to obtain the discrete point cloud of the thin-wall cylinder in the clamping state, mapping the discrete point cloud of the thin-wall cylinder in the clamping state to an ideal curved surface along the radial direction, performing triangulation network subdivision on the discrete point cloud of the curved surface in the clamping state to construct a triangular network curved surface of the cylinder in the clamping state, and constructing a triangular network unit of the ideal curved surface according to the mapping point cloud in the same topological relation. Thereby converting the mapping relation between the measuring points and the mapping points into the mapping relation between the vertexes of the curved surfaces of the two triangular meshes.
Step 2, generating an ideal pattern processing track according to the ideal curved surface in UG software, and deriving an ideal tool location point Wi(i ═ 1, 2.., n), where n is the number of knife positions, as shown in fig. 4. At a knife location W1(-1.462, 48.978, 48) (in mm) for example, the Matlab software is used to find the triangular patch Δ Q on which it is located in the ideal surface mesh according to the coordinate values of the knife location1M1N1Wherein, the triangleThe shape vertex coordinate is Q1(0,49,50)，M1(0,49,45)N1(-4.8,48.76,45), then from equation (2), the area coordinates of the knife location point in the triangular patch are:
Figure BDA0002558659820000151
triangular patch delta Q1M1N1The triangular patch is delta Q 'in the mapping of the clamped curved surface'1M′1N′1Wherein the coordinates of the vertex of the triangle are Q'1(-1.63*10-7,48.8,50)，M′1(-1.21*10-7,48.8,45)，N′1(-4.8,48.6,45) represented by formula (3), point W1In delta Q'1M′1N′1Inner mapped knife location point W'1The coordinates of (a) are:
W′i＝0.6001Q′i+0.0971M′i+0.3042N′i＝(-1.460,48.739,48)
and calculating the mapping cutter position point of each ideal cutter position point on the clamping state curved surface to obtain a mapping machining track, as shown in fig. 5.
Adopting a laser with the wavelength lambda of 532nm, the reflectivity R of the laser to the material is 0.8944, and the spot radius w at the beam waist position020 μm, liquid density ρ of the target materiallIs 8960kg/m3Enthalpy of vaporization H of target materiallv4803kJ/kg, melting enthalpy H of target materialsl205kJ/kg, ablation threshold F of the target material by the laserthIs 7 × 103J/m2Average power of laser
Figure BDA0002558659820000161
At 4.75W, the pulse repetition frequency f of the laser was 30kHz and the scanning speed v was 800 mm/min.
And 3, calculating the single-pulse ablation depth (x, z) of the material at any point on the x-z section as (unit is mum) when the defocusing amount of the single-pulse laser beam acting on the surface of the material is z according to the formulas (4) to (8):
Figure BDA0002558659820000162
when the defocus amount is z, the number N of laser pulses acting on a certain position can be calculated by equation (9):
Figure BDA0002558659820000163
the ablation cross-sectional dimension of the ablation target material under the action of N pulse lasers can be iteratively calculated through Matlab according to the formulas (10) to (17), and when the defocusing amount is 0, the maximum ablation depth of the material is 18.80 μm, and the maximum ablation width is 32.50 μm. And 3, establishing a laser ablation size prediction model according to the step 3, and solving the laser ablation depth and the ablation width under any parameter.
And 4, considering the instantaneous processing process parameter change caused by the curvature change of the curved surface, and carrying out local mapping processing track point adjustment on the pattern curve size or contour out-of-tolerance position. Fig. 6 shows a flow of the tool position adjustment routine, in which the adjacent tool position W 'is calculated from the first tool position i ═ 1 according to the formula (22) using Matlab software'1(-1.460，48.739,48)、W′2Curvature k of curved surface along feeding direction between (-1.458,48.739,48.013) (unit is mm)n＝1/R 11/449, calculating from equation (23) that during machining, the laser beam passes from knife location W'1Go to W'2In time, the initial defocusing amount z of laser processing at any position of the track0：
Figure BDA0002558659820000171
Calculating laser beam from knife location point W 'from equation (24)'1Go to W'2In the process, the actual scanning speed v':
Figure BDA0002558659820000172
by the formula (26), a cubic B-spline interpolation method is adopted, control points are inversely calculated through characteristic points, namely track points mapped to the clamped state curved surface, and the principle on the clamped state curved surface is interpolatedW 'if wanting the graphic curve of the antenna pattern'1Calculating the ideal antenna curve on the clamping state curved surface at the knife position point W 'according to the corresponding parameter value u-0'1Radius of curvature R of2：
Figure BDA0002558659820000173
Calculating a beam passing point W 'from equations (17) and (25)'1Through W'2In the process of (1), W'1、W′2Ablation depth error DE at any position of curved surface curve along feeding direction1：
DE1＝depth(x0)-depth(0)＝0
During machining by the calculation of expressions (29) to (31), the beam passes through the knife position W'1Through W'2In the process (c), the profile deviation CR between the actual machining curve and the ideal curve1，
CR1＝z3-z2＝0.15
Setting a tolerance value for the ablation depth error DE]1 μm, pattern curve profile deviation tolerance value [ CR]Is 1 μm, DE1＜[DE]，CR1＜[CR]And if the error is within the tolerance range, calculating the cutter position W 'by the same method'2、W′3Ablation depth error DE of inter-track11And the profile deviation CR of the pattern curve11Removing the redundant point W 'if the tolerance range is met'2If i is equal to i +1, continuously judging the next group of adjacent cutter location points; if DE1＞[DE]，CR1＞[CR]If the difference is exceeded, adding a knife edge point W' between two knife edge pointsu＝u'Wherein the parameter u ═ ui+ui+1) (/ 2), the W '. sup.' count can be obtained by substituting the parameter value into the formula (27)u＝u'When i is equal to n, the program loop is terminated, and finally the tool location point data meeting the precision requirement is obtained through solving, and fig. 7 is a tool location point diagram of the processing track after mapping and adjustment.
And 5, converting the adjusted tool position data into motion data of each axis of the machine tool. Fruit of Chinese wolfberryThe testing adopts a laser-five-axis machine tool combined numerical control machining system, the five-axis linkage numerical control machine tool is an A-C double-turntable type, and the directions of a cutter location point and a cutter shaft are opposite to a machine tool coordinate system OMXMYMZMAre respectively homogeneous coordinates ofMP andMorigin O of V, A axisAIn the coordinate system OMXMYMZMHas the coordinates of (U)max,Umay,Umaz) (0,0, -411.421), then OAXAYAZARelative to OMXMYMZMCan be expressed by equation (31):
Figure BDA0002558659820000181
c-axis origin OCIn the coordinate system OAXAYAZAHas the coordinates of (U)acx,Uacy,Uacz) (0,0,80), then OCXCYCZCRelative to OAXAYAZACan be expressed by equation (32):
Figure BDA0002558659820000191
OWXWYWZWrelative to OCXCYCZCCan be expressed by equation (33). To adjust the rear cutter location point P1(-1.460, 48.739,48) for example, P1And fitting a least square surface with points near the surface, and solving the normal vector and the normal vector direction of the tool position point on the surface
Figure BDA0002558659820000192
Namely the cutter shaft direction of the cutter location point under the workpiece coordinate system. General formula (34)WP＝(x y z 1)T＝(-1.460 48.739 48 1)TSecond coordinate of the direction of the cutter axisWV＝(j1j2j30)T＝(-0.0415 0.9989 0.0201 0)T. Tool coordinateIs OTXTYTZTRelative to OMXMYMZMPosition and posture of
Figure BDA0002558659820000194
The tool position point in the tool coordinate system can be expressed by the formula (35)TP and the direction of the cutter shaftTAnd V homogeneous coordinate can be expressed by an equation (36), and motion data of each axis is calculated by an inverse transformation equation (39) from a workpiece coordinate system to a machine tool coordinate system obtained by machine tool inverse kinematics transformation and a correction equation (40) of A, C angles:
Figure BDA0002558659820000193
and calculating the motion data of each axis of the machine tool corresponding to each adjusted cutter position point, thereby generating a five-axis numerical control machining program of the surface layer pattern of the clamping state curved surface.
In conclusion, the method considers the influence of the curvature change of the curved surface caused by deformation on the laser processing technological parameters of the mapping track, and combines a laser ablation size prediction model to adjust the local over-tolerance point and the redundant point of the track, so that the mapping relation between the ideal curved surface and the clamping curved surface can be quickly and accurately established, the mapping track of the ideal processing track on the clamping curved surface is obtained through solution, the laser processing track of the clamping thin-wall curved surface pattern meeting the precision requirement is finally generated, and the problem of the laser processing error of the surface pattern caused by the clamping deformation of the thin-wall curved surface piece can be effectively and reliably solved.

Claims (1)

1. A method for solving a laser processing track of a surface layer pattern of a thin-wall curved surface is characterized in that firstly, according to the characteristics of clamping deformation of a thin-wall curved surface piece, the hypothesis that the clamping deformation is mainly along the radial direction is provided, clamping state curved surface point cloud data is obtained through a three-coordinate measuring machine and is mapped to an ideal curved surface along the radial direction, a triangular mesh mapping relation of the clamping state curved surface and the ideal curved surface is respectively constructed, and a mapping track of the ideal processing track on the clamping state curved surface is solved; then, according to a laser ablation size prediction model, discretizing and solving the material ablation depth and the ablation width at any cutter position on the mapping track, considering the instantaneous process parameter change caused by the curvature change of the curved surface, carrying out local processing track point adjustment on the size of the pattern curve or the position with the out-of-tolerance outline, and finally carrying out post-processing to generate a five-axis numerical control processing track meeting the processing precision requirement; the method comprises the following specific steps:
step 1, constructing a triangular mesh mapping relation between a clamping state curved surface and an ideal curved surface
Firstly, in Ansys software, a coordinate system is established by taking the circle center of a bottom end surface (2) of a cylinder as an origin, the bottom end surface (2) of the cylinder is an XOY plane, and the axis of the cylinder is a Z axis; simulating the clamping process of the thin-wall cylinder by adopting Ansys finite element analysis software, establishing a four-node shell181 unit model in Ansys, setting material properties, and adopting a free mesh division mode; at 4 clamping points (J)1、J2、J3、J4) Applying a concentrated load, setting full constraint on the upper end surface (1) of the cylinder, and solving the current load and the result under the constraint; the post-processing interface is arranged in a cylindrical coordinate system to check results, wherein the x direction represents the radial direction, the y direction represents the tangential direction, and the z direction represents the axial direction; deriving the calculation result of the node deformation, calculating a deviation value between radial deformation and total deformation of each node, and if the deviation value is smaller than the total deformation by one order of magnitude, proposing an assumption that clamping deformation of the thin-wall cylindrical part is mainly along the radial direction;
measuring by using a three-coordinate measuring machine to obtain discrete point clouds of the thin-wall cylinder in a clamping state, and mapping the discrete point clouds to an ideal curved surface along the radial direction, so that the only mapping point of the measuring point in the ideal curved surface can be solved; performing triangulation on the discrete point cloud of the clamped curved surface, constructing a triangular mesh curved surface of the clamped cylindrical triangular mesh, and constructing a triangular mesh unit of an ideal curved surface according to the mapping point cloud in the same topological relation; thereby converting the mapping relation between the measuring points and the mapping points into the mapping relation between the vertexes of the curved surfaces of the two triangular meshes, and establishing the mapping relation between the clamped curved surface and the ideal curved surface;
step 2, solving the mapping track of the ideal track in the clamping state curved surface
Solving the upper task of the ideal curved surface mesh and the clamped curved surface mesh by the triangle affine transformation theoryA mapping relationship of a point; generating ideal tool location points on an ideal curved surface according to an original design pattern, and enabling one ideal tool location point to be Wi(i ═ 1, 2.. once, n), where n is the number of knife points, finding the triangle patch where it is located in the ideal surface mesh according to the coordinate value of knife points, and making the vertex coordinate of the triangle patch be Qi,Mi,Ni(ii) a Ideal tool location point WiAt Δ QiMiNiThe area coordinate in (A) can be expressed as Wi(λ1,λ2,λ3) Then point WiSatisfies the formula (1), and λ1+λ2+λ3＝1；
(λ1+λ2+λ3)Wi＝λ1Qi+λ2Mi+λ3Ni(1)
Point WiAnd Δ QiMiNiEach vertex will be Δ QiMiNiDivided into Δ QiMiWi，ΔMiNiWi，ΔQiNiWiHaving an area of
Figure FDA0002558659810000021
From the properties of the triangular area coordinates:
Figure FDA0002558659810000022
triangular patch delta Q in an ideal mesh surfaceiMiNiThe mapping triangular patch in the clamped state mesh surface is delta Q'iM′iN′iFrom the area coordinate invariance according to the triangle affine transformation, Δ Q can be foundiMiNiInner arbitrary knife position WiIn delta Q'iM′iN′iInner mapped knife location point W'iThe coordinates of (a) are:
W′i＝λ1Q′i+λ2M′i+λ3N′i(3)
establishing an ideal model of the thin-wall cylindrical part in UG, drawing a pattern curve on the surface of a workpiece, projecting the pattern curve on the surface of the workpiece, and generating a five-axis machining track in a curve driving mode; exporting the cutter location points, and solving mapping points of the cutter location points on the clamping state curved surface by the formulas (1) to (3) to realize the mapping of the processing track;
step 3, establishing an ablation size prediction model
Establishing a laser ablation size prediction model, facilitating subsequent discretization to solve the material ablation depth and the ablation width at any cutter position on the mapping track, and judging a track super-error point; the nanosecond laser is adopted for processing, and the distribution of laser energy density of a light beam on an x-z section can be expressed as follows:
Figure FDA0002558659810000031
wherein w is the actual spot size, F0The peak energy density for the beam acting on the x-z section is calculated by:
Figure FDA0002558659810000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002558659810000033
f is the average power of the laser, and the pulse repetition frequency of the laser;
the spot size w of the beam at any position in the z direction is expressed as:
Figure FDA0002558659810000034
in the formula, w0The size of a light spot of a light beam at the beam waist position is shown, and lambda is the wavelength of laser;
when the energy density of the pulse laser exceeds the ablation threshold of the material, the evaporation phenomenon appears on the surface of the material in the laser action area to remove the formed material, and the process conforms to the energy conservation law:
(1-R)F(x,z)-Fth＝(x,z)(ρsHsl+ρlHlv) (7)
wherein R is the reflectivity of the target material to the laser, rholIs the liquid density of the target material, HlvIs the enthalpy of vaporization of the target material, HslIs the melting enthalpy of the target material, FthThe ablation threshold of the laser on the target material is defined, F (x, z) is the energy density distribution of the beam on an x-z section, and when the defocusing amount of a single-pulse laser beam acting on the surface of the material is defined as z, the ablation depth of the material at any point on the x-z section is defined as the ablation depth of the single-pulse laser;
the single-pulse ablation depth (x, z) is then expressed as:
Figure FDA0002558659810000035
when the distance z of the light spot offset focal plane acting on the surface of the material is a negative value, the focal plane of the laser beam is above the surface of the material and is marked as negative defocusing; when z is a positive value, the focal plane of the laser beam is below the surface of the material and is marked as positive defocusing;
when the scanning speed of the pulse laser is v, the number of laser pulses N acting on a certain position is expressed as:
Figure FDA0002558659810000041
wherein int is a floor rounding function; the laser beam gradually diverges during propagation, and the divergence of the beam is expressed by the differential equation of the spot size:
Figure FDA0002558659810000042
the divergence angle theta of the laser light at a certain position (x, z)*Comprises the following steps:
Figure FDA0002558659810000043
passing through positionIs arranged (x)k-1,zk-1) Before ablation of the kth laser pulse, the defocus z of the beamk-1Expressed as:
zk-1＝z0+k-1(12)
in the formula, z0Is the initial amount of defocus of the beam,k-1is the sum of the ablation depths of the first k-1 pulses;
past the ablation site (x)k-1,zk-1) The single pulse energy distribution of the kth laser pulse of (a) is expressed as:
Figure FDA0002558659810000044
calculated ablation position (x)k-1,zk-1) Laser divergence angle theta of*(xk-1,zk-1) Expressed as:
Figure FDA0002558659810000045
the ablation is carried out along the propagation direction of the laser, passing through the ablation site (x)k-1,zk-1) The k-th laser pulse ablation depth of (a) is expressed as:
Figure FDA0002558659810000046
two spatial positions (x) before and after ablationk-1,zk-1) And (x)k,zk) The following geometrical relationships exist:
Figure FDA0002558659810000051
let N be 2N +1 and then the cross-sectional dimension of the pulsed laser ablation target material is expressed as:
Figure FDA0002558659810000052
when x is 0, the ablation depth reaches a maximum value, and the maximum ablation depth is depth (0);
the position when depth (x) is 0 is the edge of ablation outline, the distance between two side edges is maximum ablation width, let x be depth-1(x) Is the inverse function of depth (x), when depth (x) is 0, the two solutions of the inverse function are x1，x2Then the maximum ablation width is | x1-x2|；
Step 4, mapping track adjustment considering the curvature change of the curved surface
Combining an ablation size prediction model, considering instantaneous processing process parameter change caused by curved surface curvature change, and performing local mapping processing track point adjustment on the size or contour out-of-tolerance part of a pattern curve;
two adjacent knife location points W 'of mapping track'i、W′i+1The curve of the curved surface between the two surfaces along the feeding direction is simplified into a radius R1Arc of (2), mixing'i、W′i+1The inter-ideal pattern curve is simplified to radius R2The arc of (a); combining a nearest neighbor search algorithm and a least square surface fitting method to pair W'iAnd performing least square surface fitting on the adjacent points, wherein the surface parameter equation is expressed as r (u, v), and the first basic form and the second basic form of the surface r (u, v) are expressed as:
Figure FDA0002558659810000053
wherein the coefficients E, F, G, L, M, N are:
Figure FDA0002558659810000054
wherein the content of the first and second substances,
Figure FDA0002558659810000055
is curved surface r (u, v) is W'iThe unit normal vector of the point is calculated by the following formula:
Figure FDA0002558659810000061
the principal curvature and principal direction of the curved surface r (u, v) are the eigenvalues and the eigendirections of a Weingarten matrix ω, which is expressed as:
Figure FDA0002558659810000062
solving the characteristic value and the characteristic direction of the Weingarten matrix omega to obtain the maximum principal curvature k of the curved surface r (u, v)1The corresponding main direction is d1Minimum principal curvature of k2The corresponding main direction is d2(ii) a Let the feeding direction
Figure FDA0002558659810000063
And a main direction d1Is at an included angle of
Figure FDA0002558659810000064
The normal curvature in the feed direction, i.e. the adjacent cutting location W ', can be determined from the Euler equation'i、W′i+1Curvature k of curved surface between the two surfaces along the feeding directionn：
Figure FDA0002558659810000065
W'iIs taken as the origin point of the image,
Figure FDA0002558659810000066
direction x0Shaft, W'iNormal vector direction on the surface of clamped state
Figure FDA0002558659810000067
Is z1The axis is used for establishing a local dynamic plane rectangular coordinate system; during machining, the laser beam is guided from the knife position W'iGo to W'i+1In time, the initial defocusing amount z of laser processing at any position of the track0Calculated from the following formula:
Figure FDA0002558659810000068
laser beam from knife location point W'iGo to W'i+1The actual scanning speed v' of the laser is calculated by the following formula:
Figure FDA0002558659810000069
according to the laser ablation size prediction model, the calculation is iterated by Matlab software to obtain W'iTo W'i+1The ablation depth of the material at any position of the motion track of the point is depth (x)0) Ablation width of width (x)0)；
Then, during machining, the light beam is emitted from the knife position W'iThrough W'i+1In the process of (1), W'i、W′i+1The ablation depth error DE at any position along the curve of the curved surface in the feed direction is expressed as:
DE＝depth(x0)-depth(0) (25)
because the curvature of the clamping state curved surface changes, the distance between two adjacent tool positions of the processing track mapped to the clamping state curved surface also changes, and deviation, namely contour deviation, is generated between an actual processing curve and an ideal curve;
interpolating a graph curve of an ideal antenna pattern on the clamped state curved surface by using a cubic B spline interpolation method and through the characteristic points, namely the back-calculation control points of the track points mapped to the clamped state curved surface; the NURBS rational fraction form of the cubic B-spline curve is:
Figure FDA0002558659810000071
in the formula, ωi(i ═ 0, 1.. n) is a weight factor, and the first weight factor and the last weight factor are omega0,ωn> 0, the rest omegai≥0，Ai(i ═ 0, 1.. times, n) is a control point, B is a control pointi,k(u) is k-order normalized B-spline basis function, u is parameter value, and tool location Wi' corresponding parameter value is ui；
Then clamping state curved surfaceIdeal antenna curve at knife position point WiRadius of curvature R at `2Calculated from the following formula:
Figure FDA0002558659810000072
based on adjacent tool location points Wi′、W′i+1Establishing a local plane rectangular coordinate system by using an ideal curve, and then Wi′、W′i+1The inter-ideal curve equation is expressed as:
Figure FDA0002558659810000073
after processing, Wi′、W′i+1The actual curve equation between is expressed as:
z3＝width(x0)-width(0) (29)
the light beam passes through the knife position point W during machiningi'pass through W'i+1In the process of (3), the profile deviation CR between the actual machining curve and the ideal curve is expressed as:
CR＝z3-z2(30)
the tolerance value for the ablation depth error is expressed as [ DE ]]The deviation tolerance value of the curve profile of the pattern is expressed as [ CR]And the adjacent tool location point W is calculated by the Matlab software programmingi′、W′i+1Ablation depth error DE of inter-trackiAnd pattern curve profile deviation CRiAnd judging whether the distance is within the tolerance range, if the distance is out of tolerance, adding a knife position W' between the two knife positionsu＝u'Wherein the parameter u ═ ui+ui+1) And/2, continuously judging, if the cutting position is within the tolerance range, calculating the cutting position Wi′、W′i+2Ablation depth error DE of inter-trackiiAnd the profile deviation CR of the pattern curveiiRemoving the redundant point W 'if the tolerance range is met'i+1Continuously judging, and finally solving to obtain the tool location point data meeting the precision requirement;
step 5, solving and generating five-axis numerical control machining track based on machine tool forward and inverse kinematics
In order to convert the adjusted tool position data into the motion data of each axis of the machine tool, forward and inverse kinematics solution is required to be carried out on the laser-five-axis numerical control machine tool system; o isMXMYMZMFor a coordinate system fixedly connected with the machine tool body, the tool location point and the tool shaft direction are relative to the machine tool coordinate system O in kinematic transformationMXMYMZMAre respectively homogeneous coordinates ofMP andMv; the laser processing is non-contact processing without a solid cutter, and the cutter shaft direction is the laser beam propagation direction;
OAXAYAZAis a coordinate system fixedly connected with the fixed axis A, and has an origin OAIn the coordinate system OMXMYMZMHas the coordinates of (U)max,Umay,Umaz) O when the machine moves to the (X, Y, Z, A, C) positionAXAYAZAWill rotate around its own X-axis by an angle-A, OAXAYAZARelative to OMXMYMZMPosition and posture of
Figure FDA0002558659810000082
Comprises the following steps:
Figure FDA0002558659810000081
OCXCYCZCis a coordinate system fixedly connected with the fixed axis C, the origin OCIn the coordinate system OAXAYAZAHas the coordinates of (U)acx,Uacy,Uacz) O when the machine moves to the (X, Y, Z, A, C) positionCXCYCZCWill rotate around its own Z axis by an angle of-C, then OCXCYCZCRelative to OAXAYAZAPosition and posture of
Figure FDA0002558659810000091
Comprises the following steps:
Figure FDA0002558659810000092
OWXWYWZWfor a coordinate system of the workpiece fixedly connected to the workpiece, origin OWAnd OCCoincidence, then OWXWYWZWRelative to OCXCYCZCPosition and posture of
Figure FDA0002558659810000093
Comprises the following steps:
Figure FDA0002558659810000094
homogeneous coordinates of the tool location point and the tool shaft direction in the workpiece coordinate systemWP andWv is respectively:
Figure FDA0002558659810000095
for the adjusted cutter location point, the cutter axis direction needs to be solved; a certain knife position point Pi(x, y, z) and points nearby fit the least square surface, and the normal vector of the tool location point on the surface and the normal vector direction are solved
Figure FDA0002558659810000096
The cutter position point is the cutter shaft direction under the workpiece coordinate system;
OTXTYTZTfor a tool coordinate system fixedly connected to the laser, OTXTYTZTRelative to OMXMYMZMPosition and posture of
Figure FDA0002558659810000097
Comprises the following steps:
Figure FDA0002558659810000098
homogeneous coordinate of tool location point and tool shaft direction in tool coordinate systemTP andTv is respectively:
Figure FDA0002558659810000099
and respectively mapping the tool location points from the tool coordinate system and the workpiece coordinate system to the machine tool coordinate system through homogeneous transformation:
Figure FDA0002558659810000101
solving to obtain the homogeneous coordinates of the cutter location point and the cutter shaft direction under the workpiece coordinate systemWP andWv is respectively:
Figure FDA0002558659810000102
obtaining an inverse transformation formula from a workpiece coordinate system to a machine tool coordinate system through machine tool inverse kinematics transformation:
Figure FDA0002558659810000103
wherein, the motion range of the A axis is-5 degrees to 95 degrees, the angle of the C axis can be any value, and in order to avoid the solution of the A from exceeding the motion range or the discontinuity of the machine tool rotation angle C caused by multiple solutions of the angle of the C axis, the A, C angle is corrected as follows:
Figure FDA0002558659810000104
and (4) converting the adjusted tool position data into motion data of each axis of the machine tool by the formulas (39) - (40) to further generate a five-axis numerical control machining program of the surface layer pattern of the clamped curved surface.
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CN112116590B (en) * 2020-10-09 2024-04-02 北方工业大学 Method for identifying machining boundary of out-of-tolerance region of complex curved surface part
CN112116590A (en) * 2020-10-09 2020-12-22 北方工业大学 Method for identifying machining boundary of out-of-tolerance area of complex curved surface part
CN112783164A (en) * 2020-12-29 2021-05-11 北京配天技术有限公司 Track generation method and device, electronic equipment and storage medium
CN112783164B (en) * 2020-12-29 2023-08-11 北京配天技术有限公司 Track generation method and device, electronic equipment and storage medium
CN113386149A (en) * 2021-05-14 2021-09-14 中国航发北京航空材料研究院 Exhaust casing-oriented laser peening robot motion trajectory control method
CN113386149B (en) * 2021-05-14 2022-06-28 中国航发北京航空材料研究院 Movement track control method of laser shot blasting robot for exhaust casing
CN113932730A (en) * 2021-09-07 2022-01-14 华中科技大学 Detection apparatus for curved surface panel shape
CN113741337A (en) * 2021-09-10 2021-12-03 哈尔滨工业大学 Planning method and device for machining track of all-surface uniformly-distributed micro-pit structure of thin-wall spherical shell type micro component
CN113741339A (en) * 2021-09-13 2021-12-03 浙江大学高端装备研究院 Curved surface parameter domain self-adaptive partitioning method based on numerical control interpolation mapping
CN114001683B (en) * 2021-10-26 2022-09-20 大连理工大学 Complex component machining residual wall thickness self-adaptive compensation method based on coordinate origin translation
CN114001683A (en) * 2021-10-26 2022-02-01 大连理工大学 Complex component machining residual wall thickness self-adaptive compensation method based on coordinate origin translation
CN114117841A (en) * 2021-11-02 2022-03-01 哈尔滨工业大学 Nanosecond laser ablation aluminum alloy pit depth simulation model establishing method
CN114117841B (en) * 2021-11-02 2024-05-07 哈尔滨工业大学 Nanosecond laser ablated aluminum alloy pit depth simulation model establishment method
CN114115123A (en) * 2021-11-16 2022-03-01 上海交通大学 Parameterized numerical control machining method and system for large-scale aviation thin-wall non-rigid part
CN114115123B (en) * 2021-11-16 2024-04-09 上海交通大学 Parameterized numerical control machining method and system for aviation large thin-wall non-rigid part
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CN114417524A (en) * 2021-12-27 2022-04-29 西北工业大学 Method for analyzing dimensional accuracy and visualizing AR (augmented reality) based on point cloud thin-wall cylinder

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